Oh, dear, I'm afraid there are some serious obstacles to overcome. First, Muslim women cannot marry non-Muslim men. Secondly, Qatari women cannot marry non-Qataris without parental, family and government approval. If she is under 25 she cannot leave the country without her father's/brother's permission. If she were to do any of these things she could not come back to Qatar. In addition, no Qatari can hold dual citizenship. I suggest the two of you have a good, long talk before embarking on a move that would cut her off from her parents, family, religion and country.
Mandi